Two wires are fixed on a sonometer wire. Their tensions are in the ratio $$8$$:$$1$$, the lengths in the ratio $$36$$:$$35$$, the diameters in the ratio $$4$$:$$1$$ and the densities in the ratio $$1$$:$$2$$. Find the frequency of the beats (in$$ $$Hz) produced if the note of the higher pitch has frequency of $$360$$ Hz.

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Infinity Learn · Accepted Answer

For the two wires, we $$haven1=12l1T1$$$$π$$$$r12$$ρ$$1$$ and $$n2=12l2T2$$$$π$$$$r22$$ρ$$2$$⇒$$n1n2=l2l1T1T2r2r12$$ρ$$2$$ρ$$1$$   …………….(i)According$$ to the given $$probleml1l2=3635$$;$$T1T2=81$$;$$r1r2=41$$ and ρ$$1$$ρ$$2=12Substituting$$ these values in Eq. $$(1) or  $$n1n2=353681116$$⋅$$21=3536$$   …………(ii)lt$$ is clear from Eq. $$(ii) that, has higher pitch so, $$n2$$ $$=$$ $$360Now$$ $$n1360=3536$$ or $$n1=350HzThus$$ beat frequency is given asΔ$$n=360$$−$$350=10Hz$$

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